The pressure variation in a static fluid depends only on depth, which is represented by the equation: $$P=P_0+\rho_{water} gz\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space(1)$$
When an object is submerged in a static fluid, the pressure at a point below the object is not affected by the presence of the object, i.e., $$P_{below}=P_0+\rho_{water} gz\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space(2)$$, in which z is the depth to that point.
My question is: in equation (2), why is the density of the water not replaced by the density of the object, i.e., $$P_{below}=P_0+\rho_{object} gh+\rho_{water} gz_{water }\space \space\space\space\space\space\space\space\space\space(3) $$, in which $h$ is the height of the object and $z_{water}$ is the depth to the top of the object.